Monday, February 04, 2008

UC Riverside philosophy grad student Alan Moore pointed out these YouTube videos to me, of a fellow (Daniel Tammet) who recites pi from memory to more than 20,000 places without error. The videos also show him doing multiplication in his head into the hundreds of millions.

Oddly, the eminent neuroscientist V.S. Ramachandran, whom Tammet travels to San Diego to visit, does fairly little with him. (His student gets more air time.) Ramachandran could just have been too busy, but I'd have thought he'd have more to say. Hmmm....

The videos are fun and suggestive, but I'm also struck at how creduluous the researchers (Ramachandran less than others, maybe) seem to be about Tammet's phenomenological reports of how he does such incredible calculations -- by fitting together imaginary shapes in his head. Is it even topologically possible to model multiplication in this way? That's not obvious. And the direction of causation is open to question -- do the images lead to the answers or do the answers lead to images?

All that said, this is the kind of radically different capacity that gives some credibility to claims of radically different phenomenology, unlike most of the time when people claim radically different phenomenology (no imagery vs. tons of it, for example) with no behavioral differences to show for it....

5 comments:

KenF
said...

I enjoyed his book (born on a blue day), but I am inclined to agree, he's pretty vague about how the computations work. Using imagery to remember the numbers of pi, though, seems to make more sense. He also talks about how individual numbers have a strong personality for him, that seems reasonable to me. Who knows.

I'm glad you mentioned Luria's mnemonist. The bit of the YouTube videos I watched soundly sort of like the twins from Sacks's The Man Who Mistook His Wife for a Hat.

It doesn't seem that surprising that the description of computation would be vague. it is possible that there isn't a good vocabulary for talking about computation in that way. Reports from people with synaesthesia or autism seem to generally indicate that it is difficult to describe the phenomenology of manipulation of abstract objects in a way that makes sense to people without the particular ability. Even a great communicator like Feynman had some trouble describing it when he did.

If we set those issues aside though, is there much literature on the phenomenology of computation or of proof or of math generally? What Tammet says sounds different than what one would expect, but how different is it from what the phenomenology of mathematicians doing math?

Good question, Shawn! I don't know that literature at all, except for Feynman's famous remarks -- or even if there is a literature other than a few scattered comments. It would be an interesting issue to explore more fully.

I practiced doing square roots and other such mathematical functions in my head using visualization of shapes, after seeing it mentioned on 'Malcolm in the middle". At least for some purposes it worked pretty well so I think it works.

maybe I should do a bit more thought about how I did it and see if I can explain it... Bad news is I am probably not as bright as I used to be.

Anyway, I don't do that normally / instinctively - so I'm inclined to think that you can learn to do it. maybe it should be taught in schools?

rather like how I used the creating a picture story method to remember cards in a deck, which also worked OK but took more time than just 'remembering',so I don't use it normally, I'm told it gets easier with training.

When i was younger I would try to do tricks with maths - but I'd just use a simple model, memorization of key numbers (like e) and certain benchmarks (e.g. for multiplication it might be that 3x3=9 and 2x2=4 so 3x2 is between those modeled on a certain sort of curve - not that it would be useful in that case of course) fortified with a lot of instinct for guessing the curve. That's my natural methodology..

About Me

Eric Schwitzgebel
Professor of Philosophy at University of California at Riverside. Visit my homepage (link below) to view most of my philosophical and psychological essays. Email me if you like at eschwitz at domain- ucr.edu